这个方程是严格可解的，解出来应该是螺旋线
A = 3;
B = 2;
c = 1;
\[Kappa] = A/c^2;
\[Tau] = B/c^2;
r[s_] := {x[s], y[s], z[s]};
t[s_] = r'[s];
n[s_] = t'[s]/\[Kappa];
b[s_] = Cross[t[s], n[s]];
NDSolveValue[t'[s] == \[Kappa] n[s],
n'[s] == -\[Kappa] t[s] + \[Tau] b[s], b'[s] == -\[Tau] n[s],
r[0] == {A, 0, 0}, r'[0] == {0, A/c, B/c},
r''[0] == {-A/c^2, 0, 0},
r'''[0] == {0, -A/c^3, 0}, {x, y, z}, {s, 0, 2 \[Pi]}]

NDSolveValue用法错误。
各方程应构成方程列表放在第一参数。